Analysis Group
Faculty:
Lolina Alvarez Harmonic
and Functional Analysis: Function
spaces, pseudo-differential operators, interplay between harmonic analysis
and distribution theory.
Emeritus Prof. Dick Bagby Real and Harmonic Analysis: Classical analysis in Euclidean space. Convolution and Fourier multipliers. Continuity properties of operators and bounds for maximal functions in terms of function space norms. Questions of pointwise convergence.
Tiziana Giorgi Non-linear Partial Differential Equations: existence, uniqueness (up to a guage) and stability of minimizers to energy funtionals with applications to superconductivity.
Doug Kurtz Harmonic Analysis: maximal functions, singular integrals, multipliers, Littlewood-Paley operators, weighted norm inequalities.
Joe Lakey Harmonic Analysis: time-frequency analysis, wavelets, information theory and applications to signal processing, discrete dynamical systems.
Maria Cristina Mariani Nonlinear Partial Differential Equations: Nonlinear partial differential equations with applications to Physics and Finance, Stochastic processess, Statistical Mechanica, Mathematical Physics, Neural Networks.
Adam Sikora Linear Partial Differential Equations and Harmonic Analysis, Analysis, Lie groups: singular integrals, spectral and Fourier multiplier theorems, Bochner-Riesz summability, functional calculi and spectral analysis of elliptic and sub-elliptic differential operators, spectral analysis of operators with periodic or almost periodic coefficients, Riesz transforms, semi-groups of operators and heat kernels, wave equation.
Robert Smits Stochastic and Harmonic Analysis: stochastic differential equations, spectral theory, asymptotic analysis, heat kernels, large deviations, mathematical finance, eigenvalue estimates.
Christopher Stuart Functional Analysis: uniform boundedness principles, barrelled spaces, the topological vector space properties of sequence spaces.
Emeritus Prof. Chuck Swartz Functional Analysis: topological vector spaces, infinite matrices and gliding hump properties in sequence and function spaces, vector and operator valued series, vector valued measures and integrals.
Caroline Sweezy Harmonic Analysis, Complex Analysis, Applications to Partial Differential Equations: weighted inequalities for parabolic and elliptic functions on nonsmooth domains, atomic spaces between H^1 and L^1, Carleson measure conditions, square functions and the exponential square class.
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Doctoral Students:
Michael Eydenberg, Scott Izu, Lloyd Moyo, Hamed Obiedat
Recent Ph.D. Graduates:
Richard Reynolds (1998), David Emery (1998), Gregg Waterman
(1998), Ying Wang (2001), Sofian Obiedat (2002).
Master's Students:
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Group Activities:
Our group has a tradition of research collaborations among
its members. We maintain a weekly Analysis Seminar, as
well as a weekly Functional Analysis Seminar, where faculty,
graduate students, colleagues from universities in the
area and visitors present talks on their research as
well as on articles of interest from different areas
of analysis. Analysis Seminar Academic Year 2002-2003
With the support of the National Science Foundation, our group organizes the annual New Mexico Analysis Seminar jointly with analysts from the University of New Mexico.